I will review the history of analyzing stability and convergence of Galerkin
methods including Finite Element methods. We will start with the main points
of Babuska's Theorem and then review the history of the struggle from
Ritz and Rayleigh, through Galerkin, Bubnow and Petrov, asymptotic stability
result of Mikhlin, concept of optimal testing of Barret and Morton,
stabilized methods including SUPG, bubble methods, DG methods and, finally,
minimum residual methods including the DPG method.